The delay lock loop (DLL) was first described by the present inventor in the technical literature in 1961. In some sense it can be viewed as a generalization of the phase lock loop where the delay correction signal for the tracking loop is formed by the product of the received signal s(t+.epsilon.) with a differentiated reference signal s'(t). For a sinewave, of course, this operation corresponds to multiplying the received signal, cos (.omega..sub.o +.phi.), with the differentiated signal which of course is .omega..sub.O sin (.omega..sub.o t+.phi.). If the received signal has delay .tau. and the reference signal uses the estimate of delay .tau. (or .phi.), the low pass output of the multiplier gives a delay or phase correction signal for small error of EQU cos (.omega..sub.o (t+.tau.)+.phi.) sin (.omega..sub.o (t+.tau.)+.phi.).congruent..omega..sub.O .epsilon.+. . . for .omega..sub.o .epsilon.&lt;&lt;1
where .epsilon.=.tau.-.tau. as in the commonly used phase lock loop. Likewise, in the delay lock loop the product of the received signal and the differentiated reference has a low pass output EQU s(t+.tau.) s'(t+.tau.).congruent.R'(.epsilon.)+. . . .congruent.R"(0).epsilon.for small .epsilon.
Thus, in both examples the tracking loop recovers a component that is directly proportional to delay error. If the value of .tau. should suddenly increase the value of .epsilon. increases and the DLL increments .tau. to a larger value to track the received signal delay .tau..
The quasi-coherent delay lock loop can be likened to a generalization of the Costas Loop for tracking sinusoidal signals (see Spilker "Digital Communications by Satellite", 1977) for data modulated signal wherein one channel is phase shifted by 90.degree. with respect to the other. If the sine wave is biphase data modulated by d(t) then the product of the in-phase and quadrature channels is EQU [d(t) cos (.omega..sub.o (t+.tau.)+.phi.][d(t) sin (.omega..sub.o (t+.tau.)+.phi.)].congruent.sin .omega..sub.o .epsilon..congruent..omega..sub.0 .epsilon.+. . .
where the d.sup.2 (t) =1 term cancels.
In the quasi-coherent DLL we form the two products of punctual channels for the in-phase, I, received signal EQU [d(t)s(t+.tau.) cos .omega..sub.o t+.phi.][s(t+.tau.)].congruent.d(t)R(.epsilon.) cos (.omega..sub.o t+.phi.)+. . .
and the corresponding in-phase tracking channel product is EQU e.sub.I (t)=[d(t)s(t+.tau.) cos (.omega..sub.o (t+.tau.)+.phi.)][s'(t+.tau.)].congruent.d(t)R'(.tau.) cos (.omega..sub.o (t+.phi.)+. . .
The product of these two in-phase terms yields EQU d.sup.2 (t)R(.epsilon.)R'(.epsilon.) cos.sup.2 (.omega..sub.o t+.phi.).congruent.R(.epsilon.)R'(.epsilon.) cos.sup.2 (.omega..sub.o t+.phi.)+. . .
Likewise, the corresponding product for the quadrature channel EQU e.sub.Q (t)=d.sup.2 (t)R(.epsilon.)R'(.epsilon.) sin.sup.2 (.omega..sub.o t+.phi.).congruent.R(.epsilon.) R'(.epsilon.) sin.sup.2 (.omega..sub.o t+.phi.)+. . .
These two products can be added together to form EQU z.sub.T =z.sub.I +z.sub.Q =R(.epsilon.)R'(.epsilon.)[cos.sup.2 (.omega..sub.o t+.phi.) +sin.sup.2 (.omega..sub.o t+.phi.)]=R(.epsilon.)R'(.epsilon.) D(.epsilon.)
where D(.epsilon.) is the discriminator characteristic and for small .epsilon. EQU D(.epsilon.).congruent.R(O)R"(O).epsilon. for small .epsilon.
Thus, the output e.sub.T contains a term directly proportional to delay error .epsilon. as desired.
The design of prior art delay lock loops has been based on the assumption that the digital modulation in the received signals has zero rise time (i.e. zero transition time between the digital signal states) and is not optimum even for that signal. Since real signals are always band-limited signals, the rise time is, in reality, always finite.
Prior art delay lock loops determine exact signal delay by comparing correlations of the input signal with reference signals which differ in time sequence by one interval at the pseudonoise chip rate (FIGS. 1a and 1b). They are characterized as coherent if early and late correlation signals are compared from signals in which the carrier frequency (or intermediate frequency) component has been removed prior to correlation, or noncoherent if the carrier phase is not known and must be included in the correlation. The present invention is characterized as "quasi-coherent", to distinguish it from conventional delay lock loops, because carrier phase information is removed only after correlation of punctual (signal) with tracking channel information.
The closest previously published tracking system related to the QCDLL has been described by Holmes, 1990, p. 481, and by Simon et al. 1985. Simon et al. describes the Modified Code Tracking Loop (MCTL) which also uses punctual, and tracking channel multipliers and forms the product of the two to form an error signal. This system also gives improved performance over the conventional noncoherent DLL. However, these references discuss only zero rise time signals and only discuss the use of a tracking channel reference which is the difference between early and late zero rise time PN codes where the early and late spacing is one PN code chip (the same separation proposed by the present inventor in a 1963 paper). These systems are all nonoptimal and the presently described QCDLL provides significant performance advantages over those previously described.